NO

Initial ITS

Start location: l3
Program variables: x^0
   0: l0 -> l1 : x^0'=x^post1, (0 == 0 /\ -1-x^post1 <= 0 /\ 2-x^1 <= 0 /\ 1-x^1 <= 0 /\ -1+x^post1 <= 0), cost: 1
   1: l1 -> l0 : x^0'=x^post2, -x^post2+x^0 == 0, cost: 1
   2: l2 -> l0 : x^0'=x^post3, (0 == 0 /\ 2-x^post3 <= 0), cost: 1
   3: l3 -> l2 : x^0'=x^post4, x^0-x^post4 == 0, cost: 1

Chained Linear Paths

Start location: l3
Program variables: x^0
   5: l0 -> l0 : x^0'=x^post2, (0 == 0 /\ -1-x^post1 <= 0 /\ 2-x^1 <= 0 /\ -x^post2+x^post1 == 0 /\ 1-x^1 <= 0 /\ -1+x^post1 <= 0), cost: 1
   4: l3 -> l0 : x^0'=x^post3, (0 == 0 /\ 2-x^post3 <= 0 /\ x^0-x^post4 == 0), cost: 1

	Eliminating location l2 by chaining:

	Applied chaining

	First rule:
	l3 -> l2 : x^0'=x^post4, x^0-x^post4 == 0, cost: 1
	Second rule:
	l2 -> l0 : x^0'=x^post3, (0 == 0 /\ 2-x^post3 <= 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^post3, (0 == 0 /\ 2-x^post3 <= 0 /\ x^0-x^post4 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 2 3
	
	Eliminating location l1 by chaining:

	Applied chaining

	First rule:
	l0 -> l1 : x^0'=x^post1, (0 == 0 /\ -1-x^post1 <= 0 /\ 2-x^1 <= 0 /\ 1-x^1 <= 0 /\ -1+x^post1 <= 0), cost: 1
	Second rule:
	l1 -> l0 : x^0'=x^post2, -x^post2+x^0 == 0, cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post2, (0 == 0 /\ -1-x^post1 <= 0 /\ 2-x^1 <= 0 /\ -x^post2+x^post1 == 0 /\ 1-x^1 <= 0 /\ -1+x^post1 <= 0), cost: 1
	
	Applied deletion

	Removed the following rules: 0 1

Simplified Transitions

Start location: l3
Program variables: x^0
   7: l0 -> l0 : x^0'=x^post1, (-1-x^post1 <= 0 /\ -1+x^post1 <= 0), cost: 1
   6: l3 -> l0 : x^0'=x^post3, 2-x^post3 <= 0, cost: 1

	Propagated Equalities

	Original rule:
	l3 -> l0 : x^0'=x^post3, (0 == 0 /\ 2-x^post3 <= 0 /\ x^0-x^post4 == 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^post3, (0 == 0 /\ 2-x^post3 <= 0), cost: 1
	
		propagated equality x^post4 = x^0
		
	Simplified Guard

	Original rule:
	l3 -> l0 : x^0'=x^post3, (0 == 0 /\ 2-x^post3 <= 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^post3, 2-x^post3 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l0 -> l0 : x^0'=x^post2, (0 == 0 /\ -1-x^post1 <= 0 /\ 2-x^1 <= 0 /\ -x^post2+x^post1 == 0 /\ 1-x^1 <= 0 /\ -1+x^post1 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post1, (0 == 0 /\ -1-x^post1 <= 0 /\ 2-x^1 <= 0 /\ 1-x^1 <= 0 /\ -1+x^post1 <= 0), cost: 1
	
		propagated equality x^post2 = x^post1
		
	Simplified Guard

	Original rule:
	l0 -> l0 : x^0'=x^post1, (0 == 0 /\ -1-x^post1 <= 0 /\ 2-x^1 <= 0 /\ 1-x^1 <= 0 /\ -1+x^post1 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post1, (-1-x^post1 <= 0 /\ 2-x^1 <= 0 /\ 1-x^1 <= 0 /\ -1+x^post1 <= 0), cost: 1
	
	Eliminated Temporary Variables via Transitive Closure

	Original rule:
	l0 -> l0 : x^0'=x^post1, (-1-x^post1 <= 0 /\ 2-x^1 <= 0 /\ 1-x^1 <= 0 /\ -1+x^post1 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post1, (-1-x^post1 <= 0 /\ -1+x^post1 <= 0), cost: 1

Step with 6

	Trace

	6[(2-x^post3 <= 0)]
	
	Blocked

	[{}, {}]

Step with 7

	Trace

	6[(2-x^post3 <= 0)], 7[(-1-x^post1 <= 0 /\ -1+x^post1 <= 0)]
	
	Blocked

	[{}, {}, {}]

Nonterm

Start location: l3
Program variables: x^0
   7: l0 -> l0 : x^0'=x^post1, (-1-x^post1 <= 0 /\ -1+x^post1 <= 0), cost: 1
   8: l0 -> LoAT_sink : (1+x^post1 >= 0 /\ -1+n >= 0 /\ 1-x^post1 >= 0), cost: NONTERM
   6: l3 -> l0 : x^0'=x^post3, 2-x^post3 <= 0, cost: 1

	Certificate of Non-Termination

	Original rule:
	l0 -> l0 : x^0'=x^post1, (-1-x^post1 <= 0 /\ -1+x^post1 <= 0), cost: 1
	New rule:
	l0 -> LoAT_sink : (1+x^post1 >= 0 /\ -1+n >= 0 /\ 1-x^post1 >= 0), cost: NONTERM

		1+x^post1 >= 0 [0]: monotonic increase yields 1+x^post1 >= 0
		
		1-x^post1 >= 0 [0]: monotonic increase yields 1-x^post1 >= 0
		
		Replacement map: {1+x^post1 >= 0 -> 1+x^post1 >= 0, 1-x^post1 >= 0 -> 1-x^post1 >= 0}

Step with 8

	Trace

	6[(2-x^post3 <= 0)], 8[(1+x^post1 >= 0 /\ -1+n >= 0 /\ 1-x^post1 >= 0)]
	
	Blocked

	[{}, {}, {8[T]}]

Refute

	Counterexample

	[ x^0=2 ] 6 [ x^0=x^0 ] 8
	
NO

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